Cosmic ray Anisotropy

Modelling of galactic carbon in an asymmetrical
heliosphere: Effects of asymmetrical modulation
M. D Ngobeni*,1, M. S. Potgieter1
1Centre
for Space Research, North-West University, 2520
Potchefstroom, South Africa
*Dept of Physics and NDT, Vaal University of Technology, 1900
Vanderbijlpark, South Africa
11-18 AUG 2011
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Introduction
•
It is now established that the geometry of the heliosphere deviates
significantly from a sphere.
•
We study the effects of an asymmetrical geometry of the heliosphere on the
modulation of galactic cosmic rays (GCRs) from solar minimum to moderate
maximum conditions.
•
We extend the study to include different modulation conditions between the
north and south heliospheric hemispheres.
•
Conclusions about the effects of the heliospheric geometry and asymmetrical
modulation conditions on GCR carbon is made.
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Heliospheric asymmetries
Opher et al.(2008)
Snyman (2007)
•
The TS in the V1 direction in 2007 was
closer to the Sun than in Dec 2004.
The crossings of the TS by V2 at 84 AU compared to 94 AU observed by V1 show that
the TS position changes dynamically and also suggest that the heliosphere is
asymmetrically shape (at least the width of the heliosheath differs with heliolatitude).
MHD modeling supports this so that we have a well defined and large nose-tail
asymmetry together with a north-south asymmetry
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Numerical TS-Drift model
Parker’s (1965) Transport Equation (TPE):
f
   K  f   V  f 
t
v D  f 
Diffusion
1
3
  V 
f
(1)t )
 Q( r , p,
 ln p
Local sources
Convection
Particle drifts
Adiabatic energy changes
f(r,p,t) is the cosmic ray distribution function.
K is the diffusion tensor [K|| from Burger et al. (2008) and Kr and K from Burger et al. (2000)]
V(r, θ) = V(r, θ)er is the solar wind velocity vector:
νD is the averaged gradient and curvature drift velocity
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In a geometry other than a sphere, the TPE is transformed (Haasbroek and Potgieter, 1997):
f(r, θ, p)
g(u, v, w)
2
2
2
2
e.g.  f   g  u   g  u

2
2 
2
r
u  r 
u r
TS and HP positions (~ 8 & ~ 22 AU asymmetry)
55°
94 AU
131 AU
125°
86 AU
109 AU
Eq. (1) in 2D (spatial) can now be written as:
,
(2)
where the primed variables are the transformed coefficients.
See: Haasbroek & Potgieter (1998); Langner & Potgieter (2005); Ngobeni & Potgieter (2011)
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Modeling Results
Testing the transport coefficients and verifying of model:
Observational and computed spectra during solar
minimum
Red: Webber &
Higbie (2009)
Black: Moskalenko et
al. (2002)
 The model reproduces reasonably well modulation of GCR carbon
at Earth and in the outer heliosphere simultaneously.
 The assumed transport coefficients are reasonable; observable
features are produced
Ngobeni & Potgieter, ASR, 2011
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Radial Intensities: Geometrical effects towards
increasing solar activity
Red: 55°
Black:125°
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Asymmetrical modulation condition
 d  1   d 1 
 1

F ( , r )  
tanh
(


90


)
F
 

 2   2 
 

(a)
12
d  7.1r
F(, r)
8
B2
Sample solutions: contours of 200 MeV during solar
minimum in an A > 0 cycle
14
10
K   F ( , r )
 B2
0.3
1 AU
6
10 AU
4
100 AU
2
0
0
14
20 40 60 80 100 120 140 160 180
100 AU
(b)
12
10 AU
F(, r)
10
8
d  7.1r 0.3
1 AU
6
4
2
0
0
20 40 60 80 100 120 140 160 180
Polar angle (degrees)
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Radial Intensities: Asymmetric modulation
combined with geometric effects during solar
minimum
Red: 55°
Black:125°
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Radial Intensities: Asymmetric modulation
combined with geometric effects during solar
maximum conditions
Red: 55°
Black:125°
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Summary and Conclusions
•
•
Geometric asymmetric effects (~8 AU in TS and ~ 22 AU in the HP positions)
between polar angles of 55° (northern hemisphere) and 125° (southern hemisphere)
only become significant deep inside the heliosheath and at energies < ~ 1.0 GeV in
A > 0 cycles for both solar minimum and maximum conditions. This feature is
however enhanced with increasing solar activity in A < 0 cycles.
The enhancement of K over the poles that is different between the two
hemispheres can produce modulation differences between 55° and 125° that cancel
or enhance geometric effects depending on the drift cycle. This feature also
becomes strong during moderate solar maximum conditions in both polarity effects.
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